## A note on the compression theorem for convex surfaces.(English)Zbl 0986.90047

Summary: Suppose $$a_ib_ic_i$$ $$(i= 1,2)$$ are two triangles of equal side lengths and lying on sphere $$\Phi_i$$ with radii $$r_1$$, $$r_2$$ $$(r_1< r_2)$$, respectively. We have proved that there is a continuous map $$h$$ of $$a_1b_1c_1$$ onto $$a_2b_2c_2$$ so that for any two points $$p$$, $$q$$ in $$a_1b_1c_1$$, $$|pq|\geq|h(p)h(q)|$$ [J. H. Rubinstein and J. F. Weng, J. Comb. Optimization 1, 67-78 (1997; Zbl 0895.90173)]. In this note we generalize this compression theorem to convex surfaces.

### MSC:

 90C27 Combinatorial optimization 90C35 Programming involving graphs or networks

Zbl 0895.90173
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